Optimization Letters

, Volume 12, Issue 2, pp 399–410 | Cite as

A weighting subgradient algorithm for multiobjective optimization

  • G. C. Bento
  • J. X. Cruz Neto
  • P. S. M. Santos
  • S. S. Souza
Original Paper


We propose a weighting subgradient algorithm for solving multiobjective minimization problems on a nonempty closed convex subset of an Euclidean space. This method combines weighting technique and the classical projected subgradient method, using a divergent series steplength rule. Under the assumption of convexity, we show that the sequence generated by this method converges to a Pareto optimal point of the problem. Some numerical results are presented.


Pareto optimality Multiobjective optimization Projected subgradient method Weighting method 



First author was supported in part by CAPES-MES-CUBA 226/2012, FAPEG 201210267000909-05/2012 and CNPq Grants 458479/2014-4, 471815/2012-8, 303732/2011-3, 312077/2014-9. The second was partially supported by CNPq Grant 305462/2014-8 and PRONEX Optimization(FAPERJ/CNPq). The third was supported in part by CNPq Grant 485205/2013-0 and PROPESQ/UFPI.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • G. C. Bento
    • 1
  • J. X. Cruz Neto
    • 2
  • P. S. M. Santos
    • 3
  • S. S. Souza
    • 3
  1. 1.IME/UFGGoianiaBrazil
  2. 2.DM/UFPITeresinaBrazil
  3. 3.CMRV/UFPIParnaíbaBrazil

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